Question

write the sum of interior angle of each polygon like traingle , quadilateral, pentagon , hexagon etc​

Answer 1

Answer:

Given:

The sequence of an equilateral triangle, square, regular pentagon and so on of regular polygons Number of side = 3, 4, 5 .

To find:

Sum of interior angles

Sum of exterior angles

1 interior angle

1 exterior angle

Solution:

Sum of interior angles

Sum of interior angles of a regular polygon of n sides

= n × [ (n - 2)180° ]/2

= (n - 2)180°

∴ Sum of interior angles of equilateral triangle (n = 3), square (n = 4), regular pentagon (n = 5), etc. are:

180°, 360°, 540°, .

Sum of exterior angles

Sum of exterior angles of a regular polygon of n sides

= n × 180° - (n - 2) × 180°

= 2 × 180°

= 360°

which is free from "n".

1 interior angle

One interior angle of triangle, square, regular pentagon etc. are,

180°/3, 360°/4, 540°/5,.

= 60°, 90°, 180°,.

1 exterior angle

One exterior angle of triangle, square, regular pentagon etc. are,

360°/3, 360°/4, 360°/5,.

= 120°, 90°, 72°,.